Прогнозирование заказов такси¶

Цели исследования:

По историческим данным о заказах такси в аэропортах построить для заказчика «Чётенькое такси» модель предсказания количества заказов на следующий час с целью привлечения водителей в пиковые часы нагрузок.

Заказчику важно значение метрики RMSE на тестовой выборке, не превышающее 48 заказов.

Ход исследования:

  • Подготовка данных
    • Загрузка и знакомство с данными
  • Анализ данных
  • Обучение моделей для предсказания количества заказов
  • Проверка выбранной модели на тестовых данных
  • Итоговый вывод

Данные лежат в файле taxi.csv. Количество заказов находится в столбце num_orders (от англ. number of orders, «число заказов»).

Результаты исследования:

  • Для достижения целей данные были ресемплированы до частоты в 1 час
  • Временной ряд нестационарен, поэтому для его анализа применена техника декомпозиции, которая позволила выявить признаки, помогающие моделям эффективнее обучаться
  • Методом кросс-валидации были обучены 4 регрессионные модели (Линейная регрессия, Случайный лес, LightGBM, CatBoost)
  • Проведено тестирование лучшей модели по метрике RMSE, полученый результаты, удовлетворяющие критерию (важно значение метрики RMSE на тестовой выборке, не превышающее 48 заказов)
  • Заказчику рекомендавана полученная модель

Подготовка данных¶

Загрузка библиотек¶

In [1]:
import pandas as pd 
import numpy as np
import matplotlib.pyplot as plt

from sklearn.model_selection import GridSearchCV, RandomizedSearchCV, train_test_split, TimeSeriesSplit
from sklearn.metrics import mean_squared_error
from sklearn.preprocessing import StandardScaler, PolynomialFeatures
from sklearn.ensemble import RandomForestRegressor
from sklearn.linear_model import LinearRegression

from catboost import CatBoostRegressor
from lightgbm import LGBMRegressor, plot_importance

from statsmodels.tsa.seasonal import seasonal_decompose

Загрузка и знакомство с данными¶

In [333]:
taxi = pd.read_csv('/home/panther/Documents/Deep Learning/datasets/taxi.csv', parse_dates=[0], index_col=[0])
In [334]:
taxi.head()
Out[334]:
num_orders
datetime
2018-03-01 00:00:00 9
2018-03-01 00:10:00 14
2018-03-01 00:20:00 28
2018-03-01 00:30:00 20
2018-03-01 00:40:00 32
In [335]:
taxi.isna().sum()
Out[335]:
num_orders    0
dtype: int64
In [336]:
taxi.info()
<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 26496 entries, 2018-03-01 00:00:00 to 2018-08-31 23:50:00
Data columns (total 1 columns):
 #   Column      Non-Null Count  Dtype
---  ------      --------------  -----
 0   num_orders  26496 non-null  int64
dtypes: int64(1)
memory usage: 414.0 KB

Проверяю упорядоченность временной шкалы:

In [337]:
taxi.index.is_monotonic_increasing
Out[337]:
True

Ресемплирую данные, объединяя заказы за каждый час:

In [338]:
taxi = taxi.resample('1h').sum()
taxi.shape
Out[338]:
(4416, 1)

Глобальные переменные:

In [339]:
figsize = (12, 6)
target_col = 'num_orders'
min_date = taxi.index.min()
max_date = taxi.index.max()

Границы временного ряда:

In [340]:
print(f'Левая граница: {min_date}')
print(f'Правая граница: {max_date}')
print(f'Длина ряда: {max_date - min_date}')
Левая граница: 2018-03-01 00:00:00
Правая граница: 2018-08-31 23:00:00
Длина ряда: 183 days 23:00:00

Общий вид временного ряда:

In [341]:
ax = taxi.plot(title='Общий график количества вызовов такси по времени', figsize=figsize)
taxi.rolling(50).mean().plot(ax=ax, color='red', linewidth=1);
ax.legend(['Количество заказов в день', 'Скользящая средняя от количества заказов']);
ax.set_xlabel('Дата');
No description has been provided for this image

Выводы, подготовка данных¶

  • Данные загружены из файла taxi.csv в датафрейм taxi с индексацией по колонке даты.
  • В файле 26496 строк с данными по количеству заказов такси в каждые 10 минут за период с 2018-03-01 по 2018-08-31
  • Проведено ресемплирование данных с аггрегацией почасовых заказов, получилось 4416 строк

Анализ данных временного ряда¶

Распределение данных и стандартные статистики¶

In [342]:
taxi.describe()
Out[342]:
num_orders
count 4416.000000
mean 84.422781
std 45.023853
min 0.000000
25% 54.000000
50% 78.000000
75% 107.000000
max 462.000000
In [343]:
ax = taxi[target_col].plot.hist(bins=50, figsize=figsize);
mean = taxi[target_col].mean(); mode = taxi[target_col].mode()[0]
ax.axvline(mean, color='black', ls='--')
ax.axvline(mode, color='blue', ls='--')
ax.text(mean+5, 200, f'$\mu\ =\ {mean:.2f}\ (среднее)$')
ax.text(mode-35, 100, f'$\mu_o\ =\ {mode:.2f}\ (мода)$', color='blue'); 
ax.set(title='Распределение количества заказов', xlabel='Заказы', ylabel='Частота');
No description has been provided for this image

Данные имеют одномодальное правоасимметричное распределение (мода меньше среднего) с длинным правым хвостом, что говорит о том, что в данных имеются пиковые значения, существенно превышающие среднее.

Временной ряд нестационарный: среднее значение количества заказов со временем растет, также растет и дисперсия (std):

Среднее количество заказов и стандартное отклонение в первой половине ряда:

In [344]:
taxi.iloc[:taxi.shape[0]//2].agg(['mean', 'std'])
Out[344]:
num_orders
mean 65.003170
std 32.899422

Среднее количество заказов и стандартное отклонение во второй половине ряда:

In [345]:
taxi.iloc[taxi.shape[0]//2:].agg(['mean', 'std'])
Out[345]:
num_orders
mean 103.842391
std 47.098376

Иллюстрация нестационарности:

In [346]:
ax = taxi.resample('1d').sum().plot(figsize=figsize)
taxi.resample('1d').sum().rolling(10).mean().plot(ax=ax, color='red')
ax.set(title='Дневной график заказов такси', xlabel='Дата', ylabel='Количество')
ax.legend(['Количество заказов в день', 'Скользящая средняя от количества заказов']);
No description has been provided for this image

Анализ сезонной декомпозиции ряда¶

Функция постройки графика декомпозиции ряда:

In [347]:
def decompose(data, period_days, plot=['Тренд', 'Сезонность', 'Остатки'], returning=False, mov_avg=0):
    
    # определение частотности ряда в типе timedelta и перевод периода (в днях) в период частоты ряда
    delta = data.iloc[:2].apply(lambda x: x.index[1] - x.index[0])[target_col]
    decomposed = seasonal_decompose(data, period=pd.to_timedelta(f'{period_days}d') // delta)
    
    dec = {'Тренд': decomposed.trend, 'Сезонность': decomposed.seasonal, 'Остатки': decomposed.resid}
    
    plt.figure(figsize=(figsize[0], figsize[1]*len(plot)))
    plt.subplots_adjust(hspace=0.3)
    
    for i, n in enumerate(plot): # в цикле динамически расширяется фигура для размещения графиков
        ax = plt.subplot(len(plot), 1, i+1)
        name = f' {n} (период окна декомпозиции: {period_days} дней)'
        dec[n].plot(title=name, ax=ax, xlabel='Дата', ylabel='Количество заказов')
        
        # если нужен график скользящей средней периода mov_avg
        if mov_avg > 0:
            dec[n].rolling(mov_avg).mean().plot(title=name, ax=ax, xlabel='Дата', ylabel='Количество заказов',
                                                color='red')
            
    # если нужно вернуть значения декомпозиции
    if returning:
        return dec['Тренд'], dec['Сезонность'], dec['Остатки']

Оценка трендовой компоненты ряда¶

In [348]:
decompose(taxi, period_days=30, plot=['Тренд'])
No description has been provided for this image

Тренд явно различим. От 60 вызовов в начале ряда количество вызовов растет до 130.

In [349]:
decompose(taxi, period_days=10, plot=['Тренд'])
No description has been provided for this image

В начале каждого месяца (кроме июля) наблюдаются провалы в количестве заказов.

При обучении модели для характеризации тренда могут пригодиться такой признак, как день года (dt.dayofyear).

Месячная сезонность¶

Пересемплирую данные из часов в дни, чтобы сезонность была различима:

In [350]:
decompose(taxi.resample('1d').sum(), period_days=30, plot=['Сезонность'], mov_avg=5)
No description has been provided for this image

Начало каждого месяца сопровождается падением относительно линии тренда, после чего идет рост до последней недели месяца, затем падение ниже линии тренда, заканчиающееся в начале следующего месяца.

Недельная сезонность¶

Данные за первые 2 недели:

In [351]:
decompose(taxi[min_date:min_date+pd.to_timedelta(30, unit='d')], 7, plot=['Сезонность'], mov_avg=5)
No description has been provided for this image
In [352]:
taxi.loc['2018-03-05'].index.day_name()[0]
Out[352]:
'Monday'

Последние 2 недели:

In [353]:
decompose(taxi[max_date-pd.to_timedelta(14, unit='d'):max_date], 7, plot=['Сезонность'], mov_avg=5)
No description has been provided for this image
In [354]:
taxi.loc['2018-08-20'].index.day_name()[0]
Out[354]:
'Monday'

Недельное пиковое значение количества вызовов приходится на понедельник. Видна зависимость высоты внутридневных пиков от дня недели. Для моделей понадобится признак дня недели: (dt.dayofweek)

Дневная сезонность¶

Первые 2 дня:

In [355]:
decompose(taxi[min_date:min_date+pd.to_timedelta(2, unit='d')], 1, plot=['Сезонность'])
No description has been provided for this image

Последние 2 дня:

In [356]:
decompose(taxi[max_date-pd.to_timedelta(2, unit='d'):max_date], 1, plot=['Сезонность'])
No description has been provided for this image

Меньше всего заказов приходится на утренние часы около 6:00, больше всего - на вечерние часы. Для обучения моделей понадобится признак часа (dt.hour)

Выводы, анализ данных временного ряда¶

  • Исследуемый временной ряд не является стационарным
  • При декомпозиции ряда, используя различные временные периоды, выявлена внутримесячная, внутринедельная и внутридневная сезонности
  • На основе выявленных характеристик временного ряда предложены новые признаки:
    • харатеризуюище тренд: день в году (dt.dayofyear)
    • харктеризующие сезонность временного ряда: день недели (dt.dayofweek), час (dt.hour)

Обучение моделей¶

Уменьшаю размер датафрейма:

In [357]:
taxi[target_col] = pd.to_numeric(taxi[target_col], downcast='integer')
taxi.info()
<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 4416 entries, 2018-03-01 00:00:00 to 2018-08-31 23:00:00
Freq: H
Data columns (total 1 columns):
 #   Column      Non-Null Count  Dtype
---  ------      --------------  -----
 0   num_orders  4416 non-null   int16
dtypes: int16(1)
memory usage: 172.2 KB

Функции для обучения моделей и формирования признаков:

In [358]:
def make_features(data, max_lag, rolling_mean_size):
    '''Функция генерации новых признаков временного ряда'''
    data.loc[:, 'day_of_year'] = data.index.dayofyear.to_numpy().astype('int16')
    data.loc[:, 'day_of_week'] = data.index.dayofweek.to_numpy().astype('int8')
    data.loc[:, 'hour'] = data.index.hour.to_numpy().astype('int8')
    
    for lag in range(1, max_lag+1):
        data[f'lag_{lag}'] = data[target_col].shift(lag).interpolate().bfill().astype('int16')

    data['rolling_mean'] = data[target_col].shift().rolling(rolling_mean_size).mean().interpolate().bfill().astype('float32')
In [359]:
def finetune(model_name, parameters, features, target, verbose=3, jobs=-1, **kwargs):
    '''Фукнция подбора гиперпараметров
    На вход принимает класс модели, решетку гиперпараметров для поиска, признаки и целевой признак
    Возвращает лучшую из натренерованных моделей, её гиперпараметры и её луший результат по метрике RMSE
    '''
    cv = GridSearchCV(model_name(**kwargs), param_grid=parameters, scoring='neg_mean_squared_error',
                            cv=TimeSeriesSplit(n_splits=5), verbose=verbose, n_jobs=jobs)
    cv.fit(features, target)  
    
    return cv.best_estimator_, cv.best_params_, np.sqrt(-cv.best_score_)

def print_cv_results(params, rmse):
    '''Выводит результаты кросс-валидации на экран'''
    print()
    print(f'Лучшие параметры модели: {params}')
    print(f'(train, CV) лучшее RMSE: {rmse:.2f}')
    print()

Генерирую признаки (параметры задержки и периода сглаживания средней подобраны экспериментально):

In [361]:
params = {'learning_rate': [0.05449], 'max_bin': [40], 'num_leaves': [32]}
test_df = taxi.copy()
best_p = []
best_rmse = 9999

for lag in range(3, 30):
    for avg in range(7, 40):
        make_features(test_df, lag, avg)
        t_features = test_df.drop([target_col], axis=1)
        t_target = test_df[target_col]

        t_features_train, t_features_test, t_target_train, t_target_test = train_test_split(
            t_features, t_target, shuffle=False, test_size=0.1)
        test_df = taxi.copy()

        _, _, rmse = finetune(LGBMRegressor, params, t_features_train, t_target_train, verbose=0)

        if rmse < best_rmse:
            best_rmse = rmse
            best_p.append((lag, avg, best_rmse))
print(best_p)
[(3, 7, 24.196688282311555), (3, 8, 24.0252403101438)]
In [362]:
make_features(taxi, 3, 8)
In [293]:
taxi
Out[293]:
num_orders day_of_year day_of_week day hour lag_1 lag_2 lag_3 rolling_mean
datetime
2018-03-01 00:00:00 124 60 3 1 0 124 124 124 52.750
2018-03-01 01:00:00 85 60 3 1 1 124 124 124 52.750
2018-03-01 02:00:00 71 60 3 1 2 85 124 124 52.750
2018-03-01 03:00:00 66 60 3 1 3 71 85 124 52.750
2018-03-01 04:00:00 43 60 3 1 4 66 71 85 52.750
... ... ... ... ... ... ... ... ... ...
2018-08-31 19:00:00 136 243 4 31 19 207 217 197 167.375
2018-08-31 20:00:00 154 243 4 31 20 136 207 217 163.500
2018-08-31 21:00:00 159 243 4 31 21 154 136 207 165.750
2018-08-31 22:00:00 223 243 4 31 22 159 154 136 164.875
2018-08-31 23:00:00 205 243 4 31 23 223 159 154 176.125

4416 rows × 9 columns

Разделение выборки на обучающую и тестовую (10% на тестовую):

In [363]:
features = taxi.drop([target_col], axis=1)
target = taxi[target_col]

features_train, features_test, target_train, target_test = train_test_split(features, target, shuffle=False,
                                                                            test_size=0.1)
In [364]:
print(f'Размер тренировочной выборки: {features_train.shape}')
print(f'Размер тестовоый выборки: {features_test.shape}')
Размер тренировочной выборки: (3974, 7)
Размер тестовоый выборки: (442, 7)

Линейная регрессия¶

In [365]:
%%time

params = {}
lr_best_model, lr_best_params, lr_best_rmse = finetune(LinearRegression, params, features_train, target_train)
print_cv_results(lr_best_params, lr_best_rmse)
Fitting 5 folds for each of 1 candidates, totalling 5 fits

Лучшие параметры модели: {}
(train, CV) лучшее RMSE: 31.74

CPU times: user 6.98 ms, sys: 7.81 ms, total: 14.8 ms
Wall time: 132 ms

Случайный лес¶

In [366]:
%%time 

params = {'max_depth': [20, 21],
          'n_estimators': [157, 158]}

rf_best_model, rf_best_params, rf_best_rmse = finetune(RandomForestRegressor, params,
                                                        features_train, target_train, random_state=42)
print_cv_results(rf_best_params, rf_best_rmse)
Fitting 5 folds for each of 4 candidates, totalling 20 fits

Лучшие параметры модели: {'max_depth': 21, 'n_estimators': 157}
(train, CV) лучшее RMSE: 24.27

CPU times: user 1.92 s, sys: 67.3 ms, total: 1.99 s
Wall time: 10.5 s

CatBoost¶

In [386]:
%%time

params = {
    'learning_rate': [0.0279, 0.028, 0.0281],
    'iterations': [1125, 1126, 1127],
    'l2_leaf_reg': [2]
    
}

cb_best_model, cb_best_params, cb_best_rmse = finetune(CatBoostRegressor, params,
                                       features_train, target_train, random_state=42)
print_cv_results(cb_best_params, cb_best_rmse)
Fitting 5 folds for each of 9 candidates, totalling 45 fits
1053:	learn: 11.1544764	total: 3.39s	remaining: 241ms
1054:	learn: 11.1492351	total: 3.39s	remaining: 238ms
1055:	learn: 11.1450321	total: 3.4s	remaining: 235ms
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[CV 3/5] END iterations=1129, l2_leaf_reg=2, learning_rate=0.0281;, score=-513.332 total time=   3.8s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 5/5] END iterations=1129, l2_leaf_reg=2, learning_rate=0.028;, score=-867.916 total time=   5.0s
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[CV 4/5] END iterations=1129, l2_leaf_reg=2, learning_rate=0.0281;, score=-547.419 total time=   3.7s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 1/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0279;, score=-501.120 total time=   2.5s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 3/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0279;, score=-514.255 total time=   5.0s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 4/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0279;, score=-559.636 total time=   5.4s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 5/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0279;, score=-861.454 total time=   6.1s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 3/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.028;, score=-514.350 total time=   5.6s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 4/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.028;, score=-542.080 total time=   4.8s
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[CV 1/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0281;, score=-496.396 total time=   3.0s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 5/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.028;, score=-867.847 total time=   5.4s
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[CV 2/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0281;, score=-502.102 total time=   3.0s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 3/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0281;, score=-513.447 total time=   4.8s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 4/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0281;, score=-547.666 total time=   5.8s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 2/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.0279;, score=-498.594 total time=   3.4s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
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[CV 5/5] END iterations=1125, l2_leaf_reg=2, learning_rate=0.0281;, score=-872.916 total time=   6.1s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 3/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.0279;, score=-514.254 total time=   3.8s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 1/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.028;, score=-489.692 total time=   3.1s
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[CV 4/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.0279;, score=-559.729 total time=   5.8s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
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[CV 2/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.028;, score=-501.522 total time=   4.1s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 1/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.0281;, score=-496.334 total time=   4.6s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 4/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.028;, score=-542.130 total time=   7.1s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
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[CV 2/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.0281;, score=-502.118 total time=   3.4s
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[CV 5/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.028;, score=-867.828 total time=   6.8s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 1/5] END iterations=1127, l2_leaf_reg=2, learning_rate=0.0279;, score=-501.041 total time=   3.9s
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[CV 4/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.0281;, score=-547.615 total time=   5.3s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
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[CV 5/5] END iterations=1126, l2_leaf_reg=2, learning_rate=0.0281;, score=-872.900 total time=   6.1s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 4/5] END iterations=1127, l2_leaf_reg=2, learning_rate=0.0279;, score=-559.700 total time=   6.2s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 2/5] END iterations=1127, l2_leaf_reg=2, learning_rate=0.028;, score=-501.428 total time=   4.5s
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[CV 5/5] END iterations=1127, l2_leaf_reg=2, learning_rate=0.0279;, score=-861.449 total time=   6.9s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 4/5] END iterations=1127, l2_leaf_reg=2, learning_rate=0.028;, score=-541.938 total time=   4.8s
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/home/panther/anaconda3/lib/python3.9/site-packages/catboost/core.py:1411: FutureWarning: iteritems is deprecated and will be removed in a future version. Use .items instead.
  self._init_pool(data, label, cat_features, text_features, embedding_features, embedding_features_data, pairs, weight,
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[CV 5/5] END iterations=1127, l2_leaf_reg=2, learning_rate=0.028;, score=-867.897 total time=   5.6s
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Лучшие параметры модели: {'iterations': 1127, 'l2_leaf_reg': 2, 'learning_rate': 0.028}
(train, CV) лучшее RMSE: 24.15

CPU times: user 3.6 s, sys: 400 ms, total: 4 s
Wall time: 54.3 s

LightGBM¶

In [389]:
%%time

params = {'learning_rate': [0.05449, 0.0545],
          'num_leaves': [32, 33, 34],
          'max_bin': [40]
}

lgbm_best_model, lgbm_best_params, lgbm_best_rmse = finetune(LGBMRegressor, params,
                                       features_train, target_train, random_state=42)

print_cv_results(lgbm_best_params, lgbm_best_rmse)
Fitting 5 folds for each of 6 candidates, totalling 30 fits

Лучшие параметры модели: {'learning_rate': 0.0545, 'max_bin': 40, 'num_leaves': 33}
(train, CV) лучшее RMSE: 23.87

CPU times: user 267 ms, sys: 4.24 ms, total: 271 ms
Wall time: 618 ms
In [390]:
training_stats = pd.DataFrame({'Модель': ['Линейная регрессия', 'Случайный лес', 'CatBoost', 'LightGBM'],
              '(train CV) RMSE': [round(x, 2) for x in [lr_best_rmse, rf_best_rmse, cb_best_rmse, lgbm_best_rmse]],
             }).set_index('Модель').sort_values(by='(train CV) RMSE')

Выводы, обучение моделей¶

  • На тренировочной выборке методом кросс-валидации были обучены модели Линейной регрессии, Случайного леса, CatBoost и LightGBM
  • Получены следующие результаты:
In [391]:
training_stats
Out[391]:
(train CV) RMSE
Модель
LightGBM 23.87
CatBoost 24.15
Случайный лес 24.27
Линейная регрессия 31.74

Заказчику рекомендуется использовать следующую модель:

In [392]:
best_model = training_stats.index[0]
best_model
Out[392]:
'LightGBM'

Тестирование моделей¶

In [393]:
models = {'LightGBM': lgbm_best_model, 
          'CatBoost': cb_best_model,
          'Линейная регрессия': lr_best_model,
          'Случайный лес': rf_best_model}
In [394]:
pred_test = models[best_model].predict(features_test)
final_test_rmse = mean_squared_error(target_test, pred_test) ** 0.5

print(f'RMSE модели {best_model} на тестовых данных составил {final_test_rmse:.2f} заказов такси.')
RMSE модели LightGBM на тестовых данных составил 42.25 заказов такси.

График предсказаний для всей тестовой выборки:

In [395]:
plt.figure(figsize=figsize)
plt.plot(target_test.index, target_test, lw=0.8) 
plt.plot(target_test.index, pd.Series(pred_test, index=target_test.index), color='green', lw=1);
plt.title('Тестовая выборка'); plt.xlabel('Дата'); plt.legend(['Фактические заказы', 'Предсказанные заказы']);
No description has been provided for this image

В большем масштабе:

In [377]:
plt.figure(figsize=(12, 6))
plt.plot(target_test['2018-08-25':'2018-08-29'].index, target_test['2018-08-25':'2018-08-29'], lw=0.8) 
plt.plot(target_test['2018-08-25':'2018-08-29'].index, 
pd.Series(pred_test, index=target_test.index)['2018-08-25':'2018-08-29'], color='green', lw=1);
plt.title('Тестовая выборка'); plt.xlabel('Дата'); plt.legend(['Фактические заказы', 'Предсказанные заказы']);
No description has been provided for this image
In [379]:
final_test_rmse < 48
Out[379]:
True

Итоговый вывод¶

  • С целью выявить лучшую модель для предсказания количества заказов на следующий час были обучены модели машинного обучения: Линейная регрессия, Случайный лес, Градиентный бустинг (CatBoost и LightGBM).
  • В результате по критерию качества предсказания ((train CV) RMSE); была сведена итоговая таблица с результатами обученных моделей:
In [380]:
training_stats
Out[380]:
(train CV) RMSE
Модель
LightGBM 23.87
CatBoost 24.15
Случайный лес 24.27
Линейная регрессия 31.74
  • Лучшей моделью по метрике RMSE оказалась:
In [381]:
best_model
Out[381]:
'LightGBM'
  • Тестирование модели показало следущие результаты:
In [382]:
print(f'RMSE модели {best_model} на тестовых данных составил {final_test_rmse:.2f} заказов такси.')
RMSE модели LightGBM на тестовых данных составил 42.25 заказов такси.
In [383]:
final_test_rmse < 48
Out[383]:
True
  • Можно заключить, что в рамках данного исследования удалось достичь показателя качества, установленного клиентом. Клиенту «Чётенькое такси» можно рекомендовать применение данной модели для целей прогнозирования на час количетва заказов такси по историческим данным.